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Simplifying -2x + -1y + -2z + 4x + -2y + 3z = 0 Reorder the terms: -2x + 4x + -1y + -2y + -2z + 3z = 0 Combine like terms: -2x + 4x = 2x 2x + -1y + -2y + -2z + 3z = 0 Combine like terms: -1y + -2y = -3y 2x + -3y + -2z + 3z = 0 Combine like terms: -2z + 3z = 1z 2x + -3y + 1z = 0 Solving 2x + -3y + 1z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 2x + -3y + 3y + 1z = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 + 1z = 0 + 3y 2x + 1z = 0 + 3y Remove the zero: 2x + 1z = 3y Add '-1z' to each side of the equation. 2x + 1z + -1z = 3y + -1z Combine like terms: 1z + -1z = 0 2x + 0 = 3y + -1z 2x = 3y + -1z Divide each side by '2'. x = 1.5y + -0.5z Simplifying x = 1.5y + -0.5z
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